Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917592465145856 |
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| author | Giraudo, Davide |
| author_facet | Giraudo, Davide |
| contents | In this note, we give sufficient conditions for the almost sure and the convergence in $\mathbb{L}^p$ of a $U$-statistic of order $m$ built on a strictly stationary but not necessarily ergodic sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05988 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences Giraudo, Davide Probability Statistics Theory In this note, we give sufficient conditions for the almost sure and the convergence in $\mathbb{L}^p$ of a $U$-statistic of order $m$ built on a strictly stationary but not necessarily ergodic sequence. |
| title | Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2309.05988 |